4. Упростите выражение 3 5 5-a -a -1--a 8 12 и найдите его значение при 4 a-- 17

$$5\frac{3}{8}a - a - 1\frac{5}{12}a = 5\frac{3}{8}a - 1a - 1\frac{5}{12}a = (5\frac{3}{8} - 1 - 1\frac{5}{12})a = (5\frac{3}{8} - 2\frac{5}{12})a = (5\frac{3 \cdot 3}{8 \cdot 3} - 2\frac{5 \cdot 2}{12 \cdot 2})a = (5\frac{9}{24} - 2\frac{10}{24})a = (4\frac{33}{24} - 2\frac{10}{24})a = 2\frac{23}{24}a$$

При $$a = \frac{4}{17}$$

$$2\frac{23}{24} \cdot \frac{4}{17} = \frac{2 \cdot 24 + 23}{24} \cdot \frac{4}{17} = \frac{48 + 23}{24} \cdot \frac{4}{17} = \frac{71}{24} \cdot \frac{4}{17} = \frac{71 \cdot 4}{24 \cdot 17} = \frac{71 \cdot 4}{6 \cdot 4 \cdot 17} = \frac{71}{6 \cdot 17} = \frac{71}{102}$$

Ответ: $$\frac{71}{102}$$